OpenStax-CNX module: m39511 1 EM radiation: wave nature and particle nature (Grade 12) * Free High School Science Texts Project This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 3.0 1 Introduction This chapter will focus on the electromagnetic (EM) radiation. Electromagnetic radiation is a self-propagating wave in space with electric and magnetic components. These components oscillate at right angles to each other and to the direction of propagation, and are in phase with each other. Electromagnetic radiation is classied into types according to the frequency of the wave: these types include, in order of increasing frequency, radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays. 2 Particle/wave nature of electromagnetic radiation If you watch a colony of ants walking up the wall, they look like a thin continuous black line. But as you look closer, you see that the line is made up of thousands of separated black ants. Light and all other types of electromagnetic radiation seems like a continuous wave at rst, but when one performs experiments with light, one can notice that light can have both wave and particle like properties. Just like the individual ants, the light can also be made up of individual bundles of energy, or quanta of light. Light has both wave-like and particle-like properties (waveparticle duality), but only shows one or the other, depending on the kind of experiment we perform. A wave-type experiment shows the wave nature, and a particle-type experiment shows particle nature. One cannot test the wave and the particle nature at the same time. A particle of light is called a photon. Denition 1: Photon A photon is a quantum (energy packet) of light. The particle nature of light can be demonstrated by the interaction of photons with matter. One way in which light interacts with matter is via the photoelectric eect, which will be studied in detail in. 2.1 Particle/wave nature of electromagnetic radiation 1. Give examples of the behaviour of EM radiation which can best be explained using a wave model. 2. Give examples of the behaviour of EM radiation which can best be explained using a particle model. * Version 1.1: Aug 3, 2011 4:42 am -0500 http://creativecommons.org/licenses/by/3.0/
OpenStax-CNX module: m39511 2 3 The wave nature of electromagnetic radiation Accelerating charges emit electromagnetic waves. We have seen that a changing electric eld generates a magnetic eld and a changing magnetic eld generates an electric eld. This is the principle behind the propagation of electromagnetic waves, because electromagnetic waves, unlike sound waves, do not need a medium to travel through. EM waves propagate when an electric eld oscillating in one plane produces a magnetic eld oscillating in a plane at right angles to it, which produces an oscillating electric eld, and so on. The propagation of electromagnetic waves can be described as mutual induction. These mutually regenerating elds travel through empty space at a constant speed of 3 10 8 m s 1, represented by c. Figure 1 4 Electromagnetic spectrum Figure 1: The electromagnetic spectrum as a function of frequency. The dierent types according to wavelength are shown as well as everyday comparisons. Observe the things around you, your friend sitting next to you, a large tree across the eld. How is it that you are able to see these things? What is it that is leaving your friend's arm and entering your eye so that you can see his arm? It is light. The light originally comes from the sun, or possibly a light bulb or burning re. In physics, light is given the more technical term electromagnetic radiation, which includes all forms of light, not just the form which you can see with your eyes. Electromagnetic radiation allows us to observe the world around us. It is this radiation which reects o of the objects around you and into your eye. The radiation your eye is sensitive to is only a small fraction of the total radiation emitted in the physical universe. All of the dierent fractions taped together make up the electromagnetic spectrum. 4.1 Dispersion When white light is split into its component colours by a prism, you are looking at a portion of the electromagnetic spectrum. The wavelength of a particular electromagnetic radiation will depend on how it was created. 4.2 Wave Nature of EM Radiation 1. List one source of electromagnetic waves. Hint: consider the spectrum diagram and look at the names we give to dierent wavelengths.
OpenStax-CNX module: m39511 3 2. Explain how an EM wave propagates, with the aid of a diagram. 3. What is the speed of light? What symbol is used to refer to the speed of light? Does the speed of light change? 4. Do EM waves need a medium to travel through? The radiation can take on any wavelength, which means that the spectrum is continuous. Physicists broke down this continuous band into sections. Each section is dened by how the radiation is created, not the wavelength of the radiation. But each category is continuous within the min and max wavelength of that category, meaning there are no wavelengths excluded within some range. The spectrum is in order of wavelength, with the shortest wavelength at one end and the longest wavelength at the other. The spectrum is then broken down into categories as detailed in Table 1. Category Range of Wavelengths (nm) Range of Frequencies (Hz) gamma rays < 1 > 3 10 19 X-rays 1-10 3 10 17-3 10 19 ultraviolet light 10-400 7, 5 10 14-3 10 17 visible light 400-700 4, 3 10 14-7, 5 10 14 infrared 700-10 5 3 10 12-4, 3 10 19 microwave 10 5 10 8 3 10 9-3 10 12 radio waves > 10 8 < 3 10 9 Table 1: Electromagnetic spectrum Since an electromagnetic wave is still a wave, the following equation that you learnt in Grade 10 still applies: c = f λ (1) Exercise 1: EM spectrum I (Solution on p. 5.) Calculate the frequency of red light with a wavelength of 4, 2 10 7 m Exercise 2: EM spectrum II (Solution on p. 5.) Ultraviolet radiation has a wavelength of 200 nm. What is the frequency of the radiation? Examples of some uses of electromagnetic waves are shown in Table 2. Category gamma rays Uses used to kill the bacteria in marshmallows and to sterilise medical equipment continued on next page
OpenStax-CNX module: m39511 4 X-rays ultraviolet light visible light infrared microwave radio waves used to image bone structures bees can see into the ultraviolet because owers stand out more clearly at this frequency used by humans to observe the world night vision, heat sensors, laser metal cutting microwave ovens, radar radio, television broadcasts Table 2: Uses of EM waves In theory the spectrum is innite, although realistically we can only observe wavelengths from a few hundred kilometers to those of gamma rays due to experimental limitations. Humans experience electromagnetic waves dierently depending on their wavelength. Our eyes are sensitive to visible light while our skin is sensitive to infrared, and many wavelengths we do not detect at all. 4.3 EM Radiation 1. Arrange the following types of EM radiation in order of increasing frequency: infrared, X-rays, ultraviolet, visible, gamma. 2. Calculate the frequency of an EM wave with a wavelength of 400 nm. 3. Give an example of the use of each type of EM radiation, i.e. gamma rays, X-rays, ultraviolet light, visible light, infrared, microwave and radio and TV waves. 5 The particle nature of electromagnetic radiation When we talk of electromagnetic radiation as a particle, we refer to photons, which are packets of energy. The energy of the photon is related to the wavelength of electromagnetic radiation according to: Denition 2: Planck's constant Planck's constant is a physical constant named after Max Planck. h = 6, 626 10 34 J s The energy of a photon can be calculated using the formula: E = hf or E = h c λ. Where E is the energy of the photon in joules (J), h is planck's constant, c is the speed of light, f is the frequency in hertz (Hz) and λ is the wavelength in metres (m). Exercise 3: Calculating the energy of a photon I (Solution on p. 5.) Calculate the energy of a photon with a frequency of 3 10 18 Hz Exercise 4: Calculating the energy of a photon II (Solution on p. 5.) What is the energy of an ultraviolet photon with a wavelength of 200 nm? 5.1 Exercise - particle nature of EM waves 1. How is the energy of a photon related to its frequency and wavelength? 2. Calculate the energy of a photon of EM radiation with a frequency of 10 12 Hz. 3. Determine the energy of a photon of EM radiation with a wavelength of 600 nm.
OpenStax-CNX module: m39511 5 Solutions to Exercises in this Module Solution to Exercise (p. 3) Step 1. We use the formula: c = fλ to calculate frequency. The speed of light is a constant 3 10 8 m/s. c = fλ 3 10 8 = f 4, 2 10 7 f = 7, 14 10 14 Hz Solution to Exercise (p. 3) Step 1. Recall that all radiation travels at the speed of light (c) in vacuum. Since the question does not specify through what type of material the Ultraviolet radiation is traveling, one can assume that it is traveling through a vacuum. We can identify two properties of the radiation - wavelength (200 nm) and speed (c). Step 2. Solution to Exercise (p. 4) c = fλ 3 10 8 = f 200 10 9 f = 1.5 10 15 Hz Step 1. Solution to Exercise (p. 4) E = hf = 6, 6 10 34 3 10 18 = 2 10 15 J Step 1. We are required to calculate the energy associated with a photon of ultraviolet light with a wavelength of 200 nm. We can use: E = h c λ Step 2. E = h c λ = ( 6, 626 10 34) 3 10 8 200 10 9 = 9, 939 10 10 J